Limits, find delta given epsilon

A positive number epsilon (e) and a limit L of a function f at a are given. Find delta such that |f(x)-L|< epsilon if 0 < |x-a| < delta. [tex]\lim_{x->5}, 1/x= 1/5, \epsilon=.05[/tex]. That implies the following [tex] |\frac{1}{x}-\frac{1}{5}|< \epsilon \mbox{ if }|x-5|<\delta[/tex]. Which implies [tex] |\frac{1}{x}-\frac{1}{5}|< .05 \\ [/tex]. Which gives [tex].15< \frac{1}{x} < .25[/tex]. Which gives [tex]6\frac{2}{6}> x > 4 \mbox{ therefore } 1\frac{2}{3} < x-5< -1[/tex]. Which does not give the correct delta. I maybe rusty on algebra, as I am studying on my own. Could someone show me how to do it correctly. Thanks for the help.